The two NUT-like solutions of Ernst equation

Abstract

By applying Ehlers transformation to Schwarzschild and Kerr solutions of Ernst equation and choosing the suitable coordinate transformations, the two NUT-like solutions, i.e., the so called NUT–Taub-like and the Kerr–NUT-like solutions are obtained which not only can, respectively, reduce to Schwarzschild and Kerr solutions when the parameter l′=0, but also can also reduce to the NUT–Taub metric and Kerr–NUT metric, respectively, when l′ satisfies the some approximation. Meanwhile it is shown that in the NUT–Taub and Kerr–NUT solutions the range of value for the parameter l interpreted as the gravomagnetic monopole cannot be arbitrary and should be confined by mass of the source to ∣l∣⪡m. Furthermore, the differences in the geometrical structure between the NUT–Taub-like and NUT–Taub solutions are discussed and the physical properties of the horizons on the Kerr–NUT-like space–time are analyzed.